Fermi energy approximation for white dwarfs

[Guffie]

Hello,

I have read several articles/websites which talk about modelling white dwarfs,

In all of these papers they state that it can be assumed the electrons have temperature zero, i.e.
T<<T_fermi.

I haven't been able to find a solid explanation of why this is approximation is possible,

Is it due to the huge degeneracies in these stars which means that each of the electrons can reside in a ground state -> so their temperature can be considered as zero?

I just think its strange that this assumption is possible considering the actual temperature of these stars is enormous.

While I'm asking about things of this topic, I have also seen people state when E_fermi>>m_e c^2 relativistic effects become important. Is this because it implies the particles are moving very quickly?

 

[Johnahh]

I believe it is due to the degeneracy pressure not allowing electrons movement. I just had a thought would the white dwarf act as a solid as such where it has energy bands instead of energy levels? is this why it glows white?

 

[DEvens]

I believe it is due to the degeneracy pressure not allowing electrons movement. I just had a thought would the white dwarf act as a solid as such where it has energy bands instead of energy levels? is this why it glows white?

Rather ironically, it glows white because of blackbody radiation. It's hot enough that the details of energy levels of the particles in the star don't make much difference. So it produces a spectrum that does not favor any particular frequency, nor have any missing frequencies. And so, it looks white.

Assuming it is white. If the temperature is too high or too low such that the peak of the blackbody curve is not in visible, it can look non-white. Colder looks red, hotter looks blue or violet.

 

[Johnahh]

where is the heat being produced in a white dwarf? I was under the assumption fusion had stopped.

 

[Guffie]

Hrm,

So your saying that, as there are a large number of degeneracies in white dwarfs, due to the pauli exclusion principle each electron is somewhat stuck in it's state as neighbouring levels are occupied, so the electrons are essentially at rest? So the mean kinetic energy is zero and hence the temperature associated to the electrons is zero?

 

[glappkaeft]

where is the heat being produced in a white dwarf? I was under the assumption fusion had stopped.

There is little or no heat being produced in white dwarfs. They do however start out very hot (up to 40000 K) and are very compact so it takes them trillions of years to cool down completely.